Entropy Bounds and Isoperimetry

Introduction and notations Poincare-type inequalities Entropy and Orlicz spaces $\mathbf{LS}_q$ and Hardy-type inequalities on the line Probability measures satisfying $\mathbf{LS}_q$-inequalities on the real line Exponential integrability and perturbation of measures $\mathbf{LS}_q$-inequalities for Gibbs measures with super Gaussian tails $\mathbf{LS}_q$-inequalities and Markov semigroups Isoperimetry The localization argument Infinitesimal version Proof of Theorem 9.2 Euclidean distance (proof of Theorem 9.1) Uniformly convex bodies From isoperimetry to $\mathbf{LS}_q$-inequalities Isoperimetric functional inequalities Bibliography.

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